3-D Vector Projection Calculator
Compute the projection of vector A onto vector B in 3-D space: proj_B(A) = (A · B / |B|²) · B. Returns the projection ve...
Everyday arithmetic, algebra, and geometry — worked out clearly.
Percentages, fractions, ratios, geometry, and the little calculations that come up all the time — with formulas you can reuse anywhere.
Compute the projection of vector A onto vector B in 3-D space: proj_B(A) = (A · B / |B|²) · B. Returns the projection ve...
Compute the nine entries of the 3-D rotation matrix that rotates by angle θ about a unit vector axis (k_x, k_y, k_z), vi...
Convert a standard-normal z-score to a percentile (cumulative probability) via the Abramowitz-Hastings rational approxim...
Compute Hedges' g — Cohen's d adjusted for small-sample bias — from the mean difference, pooled SD, and total degrees of...
Compute the area of an annulus (the region between two concentric circles) from the outer and inner radii: A = π · (R² −...
Evaluate a degree-4 polynomial at a given x using Horner's method — far fewer multiplications than naïve evaluation. Ret...
Compute the coefficient of determination R² from a Pearson correlation r: R² = r². R² × 100 % is the share of variance i...
Compute the hyperbolic functions sinh(x), cosh(x), tanh(x), and their reciprocals csch, sech, coth at a given x. Hyperbo...
Compute the volume, surface area, and inradius of a regular tetrahedron with side length a: V = a³ / (6√2); A = √3 · a²;...
Compute McNemar's chi-square statistic for paired-categorical data (e.g. yes/no before vs after a treatment in the same...
Convert a number written in any base from 2 to 36 into any other base from 2 to 36, with companion outputs in binary, oc...
Compute the logarithm of x with respect to an arbitrary base b using the change-of-base identity log_b(x) = ln(x) / ln(b...
Compute Euler's totient φ(n) — the count of integers in 1..n coprime to n — directly from the prime factorisation. Enter...
Compute the number of ordered arrangements of length r drawn from a pool of n distinct items where repetition is allowed...
Compute the number needed to treat from the absolute risk reduction (ARR = control event rate − treatment event rate). N...
Compute a normal-approximation (Wald) confidence interval for a sample proportion, given the sample proportion p̂, the s...
Compute the minimum sample size required to estimate a population mean within a target margin of error E at a chosen con...
Compute the minimum score required on a final exam to achieve a target overall course grade, given your current pre-fina...
Compute the hypergeometric PMF P(X = k) for sampling n items without replacement from a population of N containing K suc...
Compute the volume of an ellipsoid (a 3-D generalization of an ellipse) from its three semi-axis lengths a, b, c: V = (4...
Compute the five-number summary (min, first quartile Q1, median, third quartile Q3, max), interquartile range (IQR), and...
Convert 2-D Cartesian (rectangular) coordinates (x, y) to polar coordinates (r, θ): r = √(x² + y²), θ = atan2(y, x) in r...
Compute the circumcircle of a triangle given the (x, y) coordinates of its three vertices. Reports the side lengths a, b...
Compute the 2-class softmax probabilities (positive vs negative) from raw logits z₁ and z₂: p_i = exp(z_i) / [exp(z₁) +...